Provided You’re not Trivial: Adding Defaults and Paraconsistency to a Formal Model of Explanation

Let us assume that a set of sentences explains a phenomenon within a system of beliefs and rules. Such rules and beliefs may vary and this could have as a collateral effect that different sets of sentences may become explanations relative to the new system, while other ones no longer count as such. In this paper we offer a general formal framework to study this phenomenon. We also give examples of such variations as we replace rules of classical deductive logic with rules more in the spirit of da Costa’s paraconsistent calculi, Reiter’s default theories, or even a combination of them. This paper generalizes the notion of epistemic system in [6]. That notion was used to analyze the concept of explanation, using Reiter’s default theories and a specific paraconsistent logic of da Costa. Our proposal is a formal framework, GMD, based on doxastic systems, which allows us to analyze the interaction between theoretical constructs (in this case, explanations), theories and logics. We mention some obstacles, we develop the formal framework, and finally we apply it to the modeling of scientific explanation. Along the way, we try to shed light on different kinds of interaction between paraconsistency and non-monotonicity.